Noun and の adjective
れいがい
このレストランの料理は例外なくどれも美味しいです。
All the dishes at this restaurant are delicious without exception.
きわめて例外のケースをのぞいて、この病院がその手術に成功したのをほとんど見たことがありません。
Except for a few exceptional cases, I haven't actually seen this hospital successfully complete the procedure.
コウイチはいつも朝遅くまで寝ていますが、金曜日はスーツを着なくてはいけないので例外です。
Koichi usually sleeps in, but Friday is an exception because he has to wear a suit.
Something that's outside the example doesn't follow the rules. It's not what it's supposed to be (the example), it is the exception.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.